Q. What is state space?

because state space is mostly concerned with a problem, when you try to solve a problem, we have to design a mathematical structure to the problem, which can only be through variables and parameters. eg. you have given a 4-gallon jug and another 3-gallon jug. neither has measuring marker on it. you have to fill the jugs with water. how can you get exactly 2 gallons of water in to 4 gallons. here the state space can defined as set of ordered pairs integers(x,y), such that x=0,1,2,3 or 4 and y=0,1,2 or 3; x represents the number of gallons in 4 gallon jug and y represents the quantity of water in the 3-gallon jug.